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Date:   Tue, 26 Oct 2021 22:21:23 -0400
From:   Steven Rostedt <rostedt@goodmis.org>
To:     Kalesh Singh <kaleshsingh@google.com>
Cc:     surenb@google.com, hridya@google.com, namhyung@kernel.org,
        kernel-team@android.com, Jonathan Corbet <corbet@lwn.net>,
        Ingo Molnar <mingo@redhat.com>, Shuah Khan <shuah@kernel.org>,
        Masami Hiramatsu <mhiramat@kernel.org>,
        Tom Zanussi <zanussi@kernel.org>, linux-doc@vger.kernel.org,
        linux-kernel@vger.kernel.org, linux-kselftest@vger.kernel.org
Subject: Re: [PATCH v4 6/8] tracing/histogram: Optimize division by a power
 of 2
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On Tue, 26 Oct 2021 18:31:21 -0700
Kalesh Singh <kaleshsingh@google.com> wrote:

> And IIUC max_div is an arbitrary value we decide on that's <= 2^shift?
> Is there a rule of thumb for choosing this?

The way I came up with the max was to figure out at what point is it no
longer guaranteed to be accurate. That is, what number can make the
mult/shift no longer match the division.

If we have some number div that is not a power of two. At some point:

	(X * mult) >> shift != X / div

Now I simply picked

  max = 1 << shift / (mult * div - (1 << shift))

Because that will always be within the precision of the actual number.

But I believe we can make max bigger, but because that deals with
truncation, it's not simple math.

That is, the above X / div is truncated and not the real number.

I'm sure there's an algorithm somewhere that can give as the real max.

-- Steve